Based Shearlet Directivity Transform Image Denoising

The purpose of image denoising is to suppress or eliminate noise effectively while preserving edge information and nice visual effects, the current denoising methods are mainly concentrated in the transform domain, the existing denoising methods can represent images sparsely, but they are lack of multi-directional expression of images with rich directions textural properties, Shearlet transformation due to anisotropic, multi-resolution, multi-scale, multi-directional and good locality, so that it can detect and locate all the zeros dimension singularity (that point singularity), and can sparsely represent the one dimension singularity (ie linear singularity), also can adaptively track singular curve direction, ultimately, gain the most sparse image representation. In this paper, combine the rich directional properties of Shearlet transform and various threshold functions to image denoising. The main researches of this thesis are as follows:(1) Firstly, on the basis of study the excellent performances of Shearlet transform, analyzing the various directional properties at different scales in the horizontal and vertical cone of the Shearlet transform, which provides a theoretical basis for later studies.(2) An image contains rich directional information, and as it well known that the common white Gaussian noise is isotropic, after being transformed it remains isotropic in transform domain. Thus, an image denoising noise algorithm is proposed which is based on the Shearlet transform realized in frequency domain using directional properties and classic threshold functions, this paper uses three kinds of Shearlet transform which are only using horizontal shearing filter, only using vertical shearing filter and using both horizontal and vertical shearing filter combining with classic threshold methods to denoising the images with different details at different scales and various number of directions. Experimental results show that compared to the denoising algorithms using Wavelet transform at PSNR, SNR and Time values, Shearlet transform denoising algorithm based on the various directions has a higher denoising quality.(3) In order to improve the inherent defects of classic soft and hard threshold function, a SURE-based (Stein’s unbiased risk estimate) point by point threshold function is presented. The function considers the correlation between the decomposition scales, and applied to denosing the four common images combined with the three Shearlet transforms achieved in frequency domain. Experiments show that compared to the classical threshold functions, its denoising effects on PSNR values and visual effects have a promotion.(4) In order to weaken or eliminate the pseudo-Gibbs phenomenon of the Shearlet transform achieved in the frequency domain, this thesis realizes a shift-invariant Shearlet transform decomposition method, using a soft non-diagonal blocks threshold algorithm for image denoising. Choosing different block sizes and directions at each scale to denoising the images with different details, and compare the results to the denoising methods using Nonsubsampled Contourlet (NSCT) and Curvelet for the effect of denoising PSNR values and visual effects. Experimental results show that the improved algorithm results consistent with the theory values, there is a certain improvement in the PSNR values and visual effects, effectively improving the denoising effects.